A300241 - OEIS

%I #6 Mar 02 2018 14:15:26

%S 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,

%T 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,

%U 40,41,42,43,2,44,2,45,46,47,48,49,2,50,51,52,2,53,2,54,55,56,48,57,2,58,59,60,2,61,62,63,64,65,2,66,37,67,68,69,70,71,2,72,73

%N Filter sequence combining A001065(n) and A009195(n), the sum of proper divisors of n and gcd(n,phi(n)).

%C Restricted growth sequence transform of P(A001065(n), A009195(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.

%H Antti Karttunen, <a href="/A300241/b300241.txt">Table of n, a(n) for n = 1..65537</a>

%e a(65) = a(77) (= 48) because A001065(65) = A001065(77) = 19 and A009195(65) = A009195(77) = 1.

%o (PARI)

%o rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };

%o write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }

%o A001065(n) = (sigma(n)-n);

%o A009195(n) = gcd(n, eulerphi(n));

%o Aux300241(n) = (1/2)*(2 + ((A001065(n)+A009195(n))^2) - A001065(n) - 3*A009195(n));

%o write_to_bfile(1,rgs_transform(vector(65537,n,Aux300241(n))),"b300241.txt");

%Y Cf. A001065, A009195.

%Y Cf. also A300231, A300240, A300242, A300243.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 02 2018